Geometric Discrepancy

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Geometric Discrepancy

Author : Jiri Matousek
Publisher : Springer Science & Business Media
ISBN 13 : 3642039421
Total Pages : 293 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Geometric Discrepancy by : Jiri Matousek

Download or read book Geometric Discrepancy written by Jiri Matousek and published by Springer Science & Business Media. This book was released on 2009-12-02 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? This book is an accessible and lively introduction to the area of geometric discrepancy theory, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research.

Number Theory, Fourier Analysis and Geometric Discrepancy

Author : Giancarlo Travaglini
Publisher : Cambridge University Press
ISBN 13 : 1139992821
Total Pages : 251 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis Number Theory, Fourier Analysis and Geometric Discrepancy by : Giancarlo Travaglini

Download or read book Number Theory, Fourier Analysis and Geometric Discrepancy written by Giancarlo Travaglini and published by Cambridge University Press. This book was released on 2014-06-12 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between them, at the advanced undergraduate or beginning graduate level. It starts as a traditional course in elementary number theory, and introduces the reader to subsequent material on uniform distribution of infinite sequences, and discrepancy of finite sequences. Both modern and classical aspects of the theory are discussed, such as Weyl's criterion, Benford's law, the Koksma–Hlawka inequality, lattice point problems, and irregularities of distribution for convex bodies. Fourier analysis also features prominently, for which the theory is developed in parallel, including topics such as convergence of Fourier series, one-sided trigonometric approximation, the Poisson summation formula, exponential sums, decay of Fourier transforms, and Bessel functions.

A Panorama of Discrepancy Theory

Author : William Chen
Publisher : Springer
ISBN 13 : 3319046969
Total Pages : 708 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis A Panorama of Discrepancy Theory by : William Chen

Download or read book A Panorama of Discrepancy Theory written by William Chen and published by Springer. This book was released on 2014-10-07 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the different aspects of the theory. Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling and is currently located at the crossroads of number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. This book presents an invitation to researchers and students to explore the different methods and is meant to motivate interdisciplinary research.

Handbook of Discrete and Computational Geometry

Author : Csaba D. Toth
Publisher : CRC Press
ISBN 13 : 1498711421
Total Pages : 1928 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Handbook of Discrete and Computational Geometry by : Csaba D. Toth

Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth and published by CRC Press. This book was released on 2017-11-22 with total page 1928 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Geometric Discrepancy

Author : Jiří Matoušek
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.:/5 (697 download)

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Book Synopsis Geometric Discrepancy by : Jiří Matoušek

Download or read book Geometric Discrepancy written by Jiří Matoušek and published by . This book was released on 2009 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? Such questions are treated in geometric discrepancy theory. The book is an accessible and lively introduction to this area, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research. Including a wide variety of mathematical techniques (from harmonic analysis, combinatorics, algebra etc.) in action on non-trivial examples, the book is suitable for a "special topic" course for early graduates in mathematics and computer science. Besides professional mathematicians, it will be of interest to specialists in fields where a large collection of objects should be "uniformly" represented by a smaller sample (such as high-dimensional numerical integration in computational physics or financial mathematics, efficient divide-and-conquer algorithms in computer science, etc.). From the reviews: " ... The numerous illustrations are well placed and instructive. The clear and elegant exposition conveys a wealth of intuitive insights into the techniques utilized. Each section usually consists of text, historical remarks and references for the specialist, and exercises. Hints are provided for the more difficult exercises, with the exercise-hint format permitting inclusion of more results than otherwise would be possible in a book of this size ..." Allen D. Rogers, Mathematical Reviews Clippings (2001).

Discrepancy Theory

Author : Dmitriy Bilyk
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110652587
Total Pages : 225 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Discrepancy Theory by : Dmitriy Bilyk

Download or read book Discrepancy Theory written by Dmitriy Bilyk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-01-20 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory.

Number Theory, Fourier Analysis and Geometric Discrepancy

Author : Giancarlo Travaglini
Publisher : Cambridge University Press
ISBN 13 : 1107044030
Total Pages : 251 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Number Theory, Fourier Analysis and Geometric Discrepancy by : Giancarlo Travaglini

Library of Congress Subject Headings

Author : Library of Congress
Publisher :
ISBN 13 :
Total Pages : 1480 pages
Book Rating : 4.:/5 (3 download)

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Book Synopsis Library of Congress Subject Headings by : Library of Congress

Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2012 with total page 1480 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Library of Congress Subject Headings

Author : Library of Congress. Cataloging Policy and Support Office
Publisher :
ISBN 13 :
Total Pages : 1688 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Library of Congress Subject Headings by : Library of Congress. Cataloging Policy and Support Office

Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2009 with total page 1688 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applied Algebra and Number Theory

Author : Gerhard Larcher
Publisher : Cambridge University Press
ISBN 13 : 1316123820
Total Pages : 355 pages
Book Rating : 4.3/5 (161 download)

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Book Synopsis Applied Algebra and Number Theory by : Gerhard Larcher

Download or read book Applied Algebra and Number Theory written by Gerhard Larcher and published by Cambridge University Press. This book was released on 2014-12-11 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harald Niederreiter's pioneering research in the field of applied algebra and number theory has led to important and substantial breakthroughs in many areas. This collection of survey articles has been authored by close colleagues and leading experts to mark the occasion of his 70th birthday. The book provides a modern overview of different research areas, covering uniform distribution and quasi-Monte Carlo methods as well as finite fields and their applications, in particular, cryptography and pseudorandom number generation. Many results are published here for the first time. The book serves as a useful starting point for graduate students new to these areas or as a refresher for researchers wanting to follow recent trends.

Computational Geometry

Author : Mark de Berg
Publisher : Springer Science & Business Media
ISBN 13 : 3540779744
Total Pages : 388 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Computational Geometry by : Mark de Berg

Download or read book Computational Geometry written by Mark de Berg and published by Springer Science & Business Media. This book was released on 2008-03-07 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Advances in Discrete and Computational Geometry

Author : Bernard Chazelle
Publisher : American Mathematical Soc.
ISBN 13 : 0821806742
Total Pages : 480 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advances in Discrete and Computational Geometry by : Bernard Chazelle

Download or read book Advances in Discrete and Computational Geometry written by Bernard Chazelle and published by American Mathematical Soc.. This book was released on 1999 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of refereed expository and research articles in discrete and computational geometry written by leaders in the field. Articles are based on invited talks presented at the AMS-IMS-SIAM Summer Research Conference, "Discrete and Computational Geometry: Ten Years Later", held in 1996 at Mt. Holyoke College (So.Hadley, MA). Topics addressed range from tilings, polyhedra, and arrangements to computational topology and visibility problems. Included are papers on the interaction between real algebraic geometry and discrete and computational geometry, as well as on linear programming and geometric discrepancy theory.

Algorithms and Computation

Author : Kyung-Yong Chwa
Publisher : Springer
ISBN 13 : 3540493816
Total Pages : 522 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Algorithms and Computation by : Kyung-Yong Chwa

Download or read book Algorithms and Computation written by Kyung-Yong Chwa and published by Springer. This book was released on 2003-06-29 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 9th International Symposium on Algorithms and Computation, ISAAC'98, held in Taejon, Korea, in December 1998. The 47 revised full papers presented were carefully reviewed and selected from a total of 102 submissions. The book is divided in topical sections on computational geometry, complexity, graph drawing, online algorithms and scheduling, CAD/CAM and graphics, graph algorithms, randomized algorithms, combinatorial problems, computational biology, approximation algorithms, and parallel and distributed algorithms.

Lectures on Discrete Geometry

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9780387953748
Total Pages : 540 pages
Book Rating : 4.9/5 (537 download)

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Book Synopsis Lectures on Discrete Geometry by :

Download or read book Lectures on Discrete Geometry written by and published by Springer Science & Business Media. This book was released on with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Künneth Geometry

Author : M. J. D. Hamilton
Publisher : Cambridge University Press
ISBN 13 : 1108905617
Total Pages : 200 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Künneth Geometry by : M. J. D. Hamilton

Download or read book Künneth Geometry written by M. J. D. Hamilton and published by Cambridge University Press. This book was released on 2023-12-21 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This clear and elegant text introduces Künneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The latter half of the text discusses Künneth geometry from the point of view of basic differential topology, featuring both new expositions of standard material and new material that has not previously appeared in book form. This subject, which has many interesting uses and applications in physics, is developed ab initio, without assuming any previous knowledge of pseudo-Riemannian or para-complex geometry. This book will serve both as a reference work for researchers, and as an invitation for graduate students to explore this field, with open problems included as inspiration for future research.

Fourier Analysis on Polytopes and the Geometry of Numbers

Author : Sinai Robins
Publisher : American Mathematical Society
ISBN 13 : 1470470330
Total Pages : 352 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Fourier Analysis on Polytopes and the Geometry of Numbers by : Sinai Robins

Download or read book Fourier Analysis on Polytopes and the Geometry of Numbers written by Sinai Robins and published by American Mathematical Society. This book was released on 2024-04-24 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class. Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.

European Congress of Mathematics

Author : Antal Balog
Publisher : Springer Science & Business Media
ISBN 13 : 9783764354978
Total Pages : 364 pages
Book Rating : 4.3/5 (549 download)

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Book Synopsis European Congress of Mathematics by : Antal Balog

Download or read book European Congress of Mathematics written by Antal Balog and published by Springer Science & Business Media. This book was released on 1998-07-21 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua